A stochastic differential game for the inhomogeneous ∞-Laplace equation

Abstract

Given a bounded C2 domain G ⊂ Rm, functions g ∈ C(∂G,R) and h ∈ C(G,R{double-struck} \ {0}), let u denote the unique viscosity solution to the equation -2Δ∞u = h in G with boundary data g. We provide a representation for u as the value of a two-player zero-sum stochastic differential game. © Institute of Mathematical Statistics, 2010.